Single-cell RNA sequencing (scRNA-seq) is a powerful technique to analyze the transcriptomic heterogeneities at the single cell level. It is an important step for studying cell sub-populations and lineages, with an effective low-dimensional representation and visualization of the original scRNA-Seq data. At the single cell level, the transcriptional fluctuations are much larger than the average of a cell population, and the low amount of RNA transcripts will increase the rate of technical dropout events. Therefore, scRNA-seq data are much noisier than traditional bulk RNA-seq data. In this study, we proposed the deep variational autoencoder for scRNA-seq data (VASC), a deep multi-layer generative model, for the unsupervised dimension reduction and visualization of scRNA-seq data. VASC can explicitly model the dropout events and find the nonlinear hierarchical feature representations of the original data. Tested on over 20 datasets, VASC shows superior performances in most cases and exhibits broader dataset compatibility compared to four state-of-the-art dimension reduction and visualization methods. In addition, VASC provides better representations for very rare cell populations in the 2D visualization. As a case study, VASC successfully re-establishes the cell dynamics in pre-implantation embryos and identifies several candidate marker genes associated with early embryo development. Moreover, VASC also performs well on a 10× Genomics dataset with more cells and higher dropout rate.